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Molecular structure and the occurrence of smectic A and smectic c phases

W.H. de Jeu

To cite this version:

W.H. de Jeu. Molecular structure and the occurrence of smectic A and smectic c phases. Journal de

Physique, 1977, 38 (10), pp.1265-1273. �10.1051/jphys:0197700380100126500�. �jpa-00208696�

(2)

MOLECULAR STRUCTURE AND THE OCCURRENCE OF SMECTIC A AND SMECTIC C PHASES (*)

W. H. de JEU

Philips

Research

Laboratories, Eindhoven,

The Netherlands

(Reçu

le 4

avril 1977, accepté

le

6 juin 1977)

Résumé. - On étudie les

propriétés mésomorphes

de divers azobenzènes substitués en para par des chaînes n-alkyles ou

n-alkoxy.

Les

dialkylazobenzènes

non

polaires

présentent des

phases nématiques

et smectiques A. Quand on

remplace

une chaîne

alkyl

par une chaîne alkoxy (avec création

d’un moment dipolaire terminal), il y a augmentation de la tendance à

l’apparition

d’une phase

smectique

C. Ces résultats peuvent être interprétés par un modèle dipolaire de la phase smectique C et ne confirment pas

l’hypothèse

que cette phase résulte principalement d’interactions

spatiales

entre

des molécules en

configuration zig-zag.

Dans le cas d’un seul moment dipolaire terminal, l’une des

deux

possibilités

de modèle à interaction dipolaire prévoit des couches

smectiques ferroélectriques.

Cette situation

pourrait

éventuellement fournir un modèle de la phase smectique F.

Abstract. - The mesomorphic properties of various terminally alkyl and/or alkoxy substituted azobenzenes are

investigated.

The non-polar

dialkylazobenzenes

have nematic and smectic A phases.

For each alkyl group that is replaced by an alkoxy group (thus introducing an outboard

dipole

moment) the tendency to form a smectic C

phase

is increased. These results can be rationalized in terms of a

dipole

model of the smectic C phase, and do not support the idea that this phase occurs mainly because of steric interactions between zig-zag shaped molecules. In the case of only one out- board

dipole

moment there are two

possibilities

for a model with

dipole

interaction, one of which has

ferroelectric smectic layers. This situation could possibly provide a model for the smectic F phase.

Classification Physics Abstracts

61.30

1. Introduction - The various

liquid crystalline phases

are characterized

by long-range

orientational

ordering [1].

The

elongated

molecules are, on average,

aligned

with their

long

axes

parallel

to a

preferred

direction in space. In a nematic

liquid crystal

the

molecules translate

freely,

and the centres of mass are

distributed at random. Therefore the

X-ray

diffraction

pattern

contains no

sharp

reflections. Smectic

liquid crystals,

on the other

hand,

have a

layered

structure : the molecular centres are situated in a series of

equi-

distant

planes.

In the

X-ray

diffraction

pattern

a

sharp

reflection is observed

corresponding

to the

interplanar distance,

which is of the order of the molecular

length.

In the smectic A and C

phases

the distribution of the centres of mass within the

layers

is random. The w nematic

(N)

and the smectic A

phase (SJ

have the

optical properties

of a uniaxial

crystal;

the smectic C

phase (Sc)

is found to be biaxial.

During

the last few years much attention has been

given

to the nature of the intermolecular forces that (*) Part of this paper was presented at the « Conference Euro-

p6enne sur les Smectiques Thermotropes et leurs Applications »,

Les Arcs (France), 15-18 December 1975.

lead to the formation of an

SA phase [2-4]

or an

Sc phase [5-8].

A crucial

question

is whether the interac- tion between

permanent dipole

moments is

important

for the formation of the

Sc phase.

It is the purpose of this paper to

provide

a molecular basis for this dis- cussion

by investigating

the type of smectic

phases occurring

in some series of

compounds

which have

been selected because of

specific

structural differences.

Section 2

begins

with a review of the various theories for the

Sc phase,

with

emphasis

on the

presumptions

about the molecular

properties

of the constituent

compounds.

Section 3 discusses the smectic

phases occurring

in various

terminally

substituted azo- and

azoxybenzenes.

The

p,p’-di-n-alkylazobenzenes [9]

are

k a suitable

starting point

for such a

comparison

because

they

are

non-polar. By substituting alkoxy

for

alkyl and/or azoxybenzene

for

azobenzene, dipole

moments

can be introduced at

specific positions

while

only

minor variations of the molecular

shape

occur. The results

are discussed in section 4. It turns out that in these

cases the occurrence of an

Sc phase

can be understood with the aid of a

simple

extension of McMillan’s

dipole

model. Steric

repulsions

are

probably

not a dominant

effect. The extension of the

dipole theory

of the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0197700380100126500

(3)

1266

Sc phase

also

provides

a

possible

model for the

smectic F

phase.

In the literature the smectic F

phase

is

reported

to occur below an

Sc phase

upon

cooling

of

some

compounds [10].

It seems to have all the pro-

perties

of the

Sc phase (liquid layers, biaxiality, etc.)

and the ways in which it differs from the

Sc phase

have

not yet been determined.

2. Models for the smectic C

phase.

- In all models

for the smectic C

phase

it is assumed that the smectic A order is well established : there is orientational order-

ing

of the

long

molecular axes and

positional ordering

of the molecules in

layers.

If B denotes the

angle

between the

long

molecular axis and the

preferred direction,

the molecular orientation can be described

by

a distribution function

f ’(9),

where

is the

probability

that the

long

molecular axis will form

an

angle

between 0 and 6 + d0 with the

preferred

direction. The average

degree

of orientational

ordering

can be described

by

an order parameter

[1]

The distribution function

J’(0)

is related to

V(O),

the

orientation

dependent part

of the

potential, by j’(9) = (I/Z) exp(- V/kT)

where Z is a normaliza-

tion constant. In Maier and

Saupe’s theory [11]

of the

nematic

phase V(9)

is calculated in a mean-field

approximation assuming

that it comes from the ani-

sotropic part

of the

dispersion

forces. This leads to a

set of self-consistent

equations for 17

and

v(9)

that can

be solved to

give 17

versus temperature,

yielding

a NI

phase

transition at

TNI. V(O)

can be shown to be

approximately proportional

to the

squared anisotropy

of the molecular

polarizability [12].

In

practice

the

elongated

molecules often possess a skeleton of a electrons and

additionally

a central core

of dclocalizcd vr electrons.

Consequently

the

polari- zability

is to a

large

extent concentrated in the central part of the

molecule,

and therefore the molecules will

prefer

to have their central

parts

close

together.

This

effect becomes more

pronounced

if the skeleton

of Q electrons is extended. Thus in a

homologous

series

the

tendency

to form smectic

phases

increases with

increasing length

of the molecules. This is

generally accepted

to be the

origin

of the occurrence of smectic

phases, although

some curious

exceptions

have been

noted in the case of

strongly asymmetrically

substitut-

ed molecules

[13].

McMillan has made these ideas

more

quantitative

in a model that

ignores

the

polariza- bility

of the end groups, and takes a Gaussian distri- bution for the interaction between the central

parts

of

the molecules

[3].

The model

predicts

a

NSA phase

transition that may be

second-order, depending

on the

ratio between the

length

of the central aromatic core

and the total

length

of the molecule. These

predictions

are at least

qualitatively

in agreement with

experi-

mental results.

For the

Sc phase

the literature contains various models on which there is as yet no

general

agreement.

McMillan

[5]

assumes that a

primary

role is

played by

interactions between transverse permanent

dipole

moments. Unlike the situation in the N and the

SA phase,

the rotation around the

long

molecular axis cannot then be

completely

free for the functional

groups with which the

dipoles

are connected. Let us assume that the

SA

order is well

established,

and that

the molecules can be

represented by cylinders

with two

outboard

dipole

moments J1 at a distance

d/2

from the

centre

[5] (see Fig. la).

Now we consider the interac- tion between the

dipole

moments of the molecules in a

smectic

plane. The’preferred

direction is taken

along

the

z-axis,

while the

angle

between the x-axis and one

of the

dipoles

is denoted

by

9. Then the

single particle potential

can be written as

where E is the field at the

position

of a

dipole

due to the

dipoles

of the other molecules. This field

depends

on

g(r),

the

two-particle

correlation

function,

which is

simply

assumed to be

FIG. l. - Schematic representation of the dipole model (a) and of the steric model (b) of the Sc phase.

(4)

where n2 is the

particle density

in the smectic

plane.

Neglecting

the interactions between

dipoles

at different

levels,

we can then calculate E and find that it is a

function

of fi = It#,

the average value of the upper or

lower

dipole

moment. In turn

IlP

is calculated self-

consistently using

the

potential

of

equation (2).

As a

result a second-order

phase

transition

SA SC

is pre- dicted at

[5]

where k is Boltzmann’s constant and Boo the

high- frequency

dielectric

permittivity.

In this model the

Sc phase

is

predicted

to be biaxial

provided

the

constituent molecules are biaxial

[5].

If the outboard

dipoles

are not

exactly perpendicular

to the

long

molecular

axis,

but have a

component 6 along

this

axis,

there is a

torque

3

A;7cA 6fl to

tilt the molecule

over in the x direction. There will be a

restoring

torque -

K 03C8, where 4/

is the tilt

angle

and K is an

elastic constant.

Equating

the two torques and

using

the

explicit

result

for P [5]

a tilt

angle

is found

given by

Although

the

physical properties

of McMillan’s model agree well with those of the

Sc phase,

there is consi-

derable

disagreement

on the

question

of whether there is in

reality

no free rotation of the molecules around their

long

axis

[14, 15].

It should be

emphasized, however,

that the model still

permits

rotation of

parts

of the molecule not connected with the

dipole

moments. Hence

techniques

that

probe

the movement

of,

for

example,

the

phenyl rings

are of limited value in

testing

the model. In fact the model

requires

that the

various

parts

of the molecule differ in their freedom of rotation. The molecules will often possess a third central

dipole

moment which is still assumed to be

randomly

distributed. If this is not the case additional

phase

transitions are

predicted, leading

to other

phases

that are two-dimensional ferroelectrics within the smectic

layers.

Wulf

[6]

has

given

a model of the

Sc phase

in which

the

repulsive,

or

steric,

forces

play a

dominant role.

The characteristic order is assumed to be

mainly

a

result of the effect of the molecular

shape

on the

packing problem

for the

liquid.

In the case of the

Sc phase

the relevant factor is the

zig-zag

gross

shape

of the

molecules, thought

to be a result of end chains that are

symmetrically

attached to the

molecules,

and

are not collinear with the central

body

of the molecules

(see Fig. 1 b).

The model calculation starts

by writing

down an effective interaction between the molecules that

simulates,

at least

qualitatively,

the effect of the

molecular

zig-zag shape.

This interaction is then used in a mean field

calculation, assuming

that the

SA

order

is well established. Let u 1. u2 and

u3

be unit vectors in a

molecule-fixed coordinate

system, u3 being along

the

long

molecular axis. The

zig-zag

interaction between

a

pair

of molecules 1 and 2 is taken to be

[6]

The first term accounts for the fact that the molecules interfere less with one another if their

long

and

short axes

align together. Consequently,

the result-

ing Sc phase

will be biaxial if the constituent molecules

are biaxial. In this model there is no

completely

free

rotation of the molecules around their

U3

axis in the

Sc phase.

The second term in

equation (6)

repre- sents the additional

tendency

of the molecules to tilt

over with respect to the intermolecular vector r 12 ; r2 is the range of

A2(r12).

We must

require

that

0

A2(r) AI(r)

in order to ensure that the

molecules do not tilt when the

long

and short axes are

not yet

aligned.

We shall not discuss the details of the model. A second-order

phase

transition

SA Sc

is

predicted

with a tilt

angle ql growing continuously

from zero at the

transition,

and

always remaining

smaller than

Tr/4 [6].

In order to

distinguish

between

McMillan’s

dipole

model and Wulfs steric model it will be necessary to

investigate

in detail the

type

of molecules that

give

an

Sc phase.

Both models are

incompatible

with

completely

free rotation around the

long

molecular axis.

Finally

Priest

[7]

has

given

a model of the

SA Sc phase

transition

assuming

that there is an effective molecular second-rank tensor which is

responsible

for the

orientational

phenomena

in the smectic

phase.

Denot-

ing

an element of this tensor

by

qij, the average of qij

over molecules in the

vicinity

of a

point

r can be

introduced :

One can

expand

the orientational interaction energy between two molecules in a series bilinear in Q. With

appropriate

values for the

expansion

coefficients a

second-order

phase

transition

SA Sc

can be obtained.

The tilt

angle

varies as

(TeA - T)1/2

as in the other

models,

while a small

biaxiality

is induced

[7]. Contrary

to the

previous models,

the

biaxiality

is due to the

symmetry

of the

Sc phase

rather than the

Sc

tilt

being

the result of a

tendency

to form a biaxial

phase.

Note

that in

equation (7) Qij

may be uniaxial even if qij is biaxial.

However,

if qij is also

uniaxial,

free rotation around the

long

molecular axis is not forbidden in the

Sc phase.

Priest did not

give suggestions

for the

specific

tensor qij to be considered.

However,

this

point

was

recently

taken up

by

Cabib and Ben-

guigui [8],

who treated the molecules as

axially

symme- tric

objects

in both the

SA

and the

Sc phase,

and

considered the interaction between the components of the

dipole

moments

parallel

to the

long

molecular axis.

Hence their model is

complementary

to McMillan’s

dipole

model. In fact

they

suppose that each molecule

(5)

1268

has two

opposite dipoles along

the

long

axis. The

Sc phase

is induced because the molecules tend to slide

along

each other due to the electrostatic

interaction,

thus

increasing

the distance between the molecular centres.

A well-known case of an

SA SC phase

transition is found in

terephthal-bis-butylaniline [16] (TBBA),

where the tilt

angle

indeed grows with

decreasing temperature

from zero at

TCA,

as

predicted by

all the

models

given

above. There are

hardly

any other

compounds

for which this

point

has been

investigated.

In some other cases the

Sc phase

is observed

directly

below a N

phase. Usually

a

large

tilt

angle

is then

observed

(say 450), independent

of

temperature [17].

Formally

a

NSc phase

transition may be described

by combining

models for the

NSA

and the

SA Sc phase

transitions in a situation where

TAN TeA.

It is clear

that the tilt

angle

cannot then be zero at the

NSc phase transition,

and may be

approximately independent

of

temperature

if the curve

of 03C8

versus

T/T CA

saturates

with

decreasing temperature.

The maximum value of the tilt

angle

in Wulfs and in Priest’s model

(450

and

49.1 °, respectively)

is of the

right

order of

magnitude.

In McMillan’s model the maximum tilt

angle depends

on the details of the molecules.

3. Smectic

phases

of

alkyl-

and

alkoxy-substituted

azobenzenes. - First we shall discuss the nature of the

mesophases

found in the

compounds

of the series

The transition temperatures were determined with a

Leitz

Orthoplan polarizing microscope equipped

with

a Mettler FP52

heating

stage. Heats of transition were

recorded

by

means of differential

scanning calorimetry

with a Perkin-Elmer DSC IB. The results for series I and some of the

higher

members of series II are

given

in tables I and II and

displayed

in

figure

2. The

compounds

of series I have also been discussed in reference

[9],

but without

explicit

reference to the

smectic

phases.

The transition temperatures

given

TABLE I

Phase transitions

of

series I

(K

stands

for crystalline ; monotropic

transitions are

placed

between

parentheses)

e) Due to crystallization no quantitative measurement was

possible.

TABLE II

Phase transitions

of’series

II

e) Gabler, ref. [ 18], gives for this compound a monotropic SN transition at 97 °C. We could not reproduce this result, although the

N phase could be supercooled down to 94 °C. In some cases we observed a metastable cryitalline phase in the region 950-1000, which could

probably be mistaken for a smectic phase. This idea is in agreement with the fact that Gabler did not observe a smectic phase for n = 9.

(6)

FIG. 2. - Transition temperatures versus chain length for series I and II (for series II, n 6, from reference [18]).

FIG. 3. - Transition temperatures versus chain length for series III

(for n 5 from reference [24]).

here should be considered as more accurate. For the

higher

members of series

I, SA phases

occur in addition

to the N

phases.

This is

easily

established from the

simple

focal-conic or

homeotropic

textures and the

occurrence of one

sharp X-ray

reflection at small

Bragg angle

in a

powdered sample [19].

For n = 9

and n = 10 an additional

SB phase

is found. The textures of this

phase

are either blurred focal-conic or

homeotropic,

the latter

again indicating uniaxiality.

In the

powder X-ray

diffraction

pattern

two

sharp

reflections are observed

(one

at

small,

the other at

large Bragg angle).

This classification of the

SB phase

of

(I, n

=

9)

has been confirmed from its

complete miscibility

with the

known SB phase

of

N-(p-n-pentyl- benzylidene) p’-n-hexylaniline [20].

For the

higher

members of series

II, Sc phases

are

observed below the N

phases.

Under the

polarizing microscope

either broken focal-conic textures or

schlieren textures are observed. The absence of inter- ference colours in the schlieren textures indicates a

relatively large

tilt

angle directly

below the

NSc

transi-

tion. The classification of the

Sc phase

of

(II, n

=

10)

has been confirmed from its

complete miscibility

with

the known

Sc phase

of

p,p’-di-n-heptyloxyazoxy-

benzene

[21].

It is

interesting

to compare these results with those for the

correspondingly

substituted

azoxybenzenes.

The

mesophases

of the

p,p’-di-n-alkylazoxybenzenes

are described in reference

[22].

The smectic

phases

of

the

higher homologues

of this series are all

SA (simple

focal-conic or

homeotropic

textures,

complete

misci-

bility

with the

SA phase

of series

I).

The

mesophases

of

the

p,p’-di-n-alkoxyazoxybenzenes

are described in

references

[18]

and

[23].

The smectic

phases

of the

higher

members of this series are well known to be of the

Sc

type

[21].

Hence we conclude that

replacement

of the azo

linkage by

an azoxy

linkage,

thus introduc-

ing

a central

dipole

moment, does not have any influence on the type of smectic

phases

that occur in

these systems.

TABLE III

Phase transitions

oj’series

III

(7)

1270

Next we consider the

mesophases occurring

in the

series

Although

a strong

dipole

is found in this series

only

at

one

end,

the molecular

shape

is still

approximately symmetric.

The results for some of the

higher

members

of this series are

given

in table III and

figure

3. For

n = 8 and n =

9,

on

cooling

from the N

phase,

an

SA phase

is first

observed,

then an

Sc phase.

The

enthalpy

of the

SA Sc

transition is very small. The tran- sition is best observed on

cooling

a

homeotropic SA

texture. At the

SA Sc

transition a schlieren texture appears with interference colours

indicating

a tilt

angle

that grows

continuously

from zero. This is

confirmed

by conoscopic

measurements where the maltese cross observed in a

homeotropic SA sample

moves off-centre when the

SA Sc

transition is

passed.

For n = 9 one observes on

cooling

a transition to a

third smectic

phase

that was classified as

S,.

In order to

investigate

whether the

asymmetric shape

of the molecules affects certain

mesophases,

we

finally

consider the series

The various

phases

of some of the

higher

members of

the series are indicated in table IV and

figure

4. The

results are very similar to those found for series III.

TABLE IV

Phase transitions

oj’series

IV

FIG. 4. - Transition temperatures versus chain length for series IV

(for n 7 from reference [24]).

Note, however,

that for

(IV, n

=

8)

there is no

SA phase;

the

Sc phase

goes

directly

over into the N

phase.

For n = 9 an intermediate

SA phase

appears.

The

temperature

range in which the

SA phase

is

stable increases with

increasing

chain

length.

All the

mesophases

of series IV have textures similar to those

of the

corresponding mesophases

of series

III,

with

which

they

are also

completely

miscible. From the

shift of the

conoscopic

cross observed in

homeotropic samples

the tilt

angle

has been calculated for

(IV, n

=

11)

in the

vicinity

of

TCA;

the results are

given

in

figure

5. The numerical

aperture

of the

conoscope was

only

0.33 as determined

by

the conden- ser,

corresponding

to an

angular

field of view of about 400 in air. The absolute value of the tilt

angle depends

on the value of the maximum index of refrac-

FIG. 5. - Tilt angle versus relative temperature in the Sc phase

of compound (IV, n = 11).

(8)

tion,

which was assumed to be 1.7. The variation of

tilt with temperature around

T CA,

as

given

in

figure 5,

is very similar to that found in the well-known case

of TBBA.

In

general

the transition

SC SB

is

only

visible if the

Sc phase

is in a schlieren texture. With

decreasing temperature

a new schlieren texture then appears at the

transition,

which is

brighter

and has fewer

singularities.

In order to

study

this third smectic

phase

in more detail we made a mixture of 50 per cent

(by weight)

of

(III, n

=

9)

and

(IV, n

=

11).

The

transitions of this mixture are

approximately K30SB49Sc61SA73N80,

and the

SB phase supercools easily

down to room

temperature.

The

SB phase

in

this mixture also occurs as a blurred focal-conic texture that

gradually

tends to

change

into a mosaic

texture. The

powder X-ray

diffraction

pattern

contains

two

sharp

reflections without any additional structure.

Hence we conclude that the classification of this

phase

as an

SB phase

is correct. The occurrence of schlieren textures and the absence of

homeotropic

textures indicates that this

SB phase

is

probably

biaxial.

4. Discussion. - We shall first discuss the results for series I and II. The

replacement

of a

CH2

group

by

an oxygen atom has the effect of

introducing

a

dipole

moment of about 1.3

D,

at an

angle

of about 720 with

the p,p‘

axis of the

adjacent

aromatic

ring [25], giving

a

dipole component

of about 0.4 D

along

the

p,p’

axis.

In the case of an

alkyl

group there is a

dipole

moment

of 0.4 D

along

this

p,p’

axis. Hence the

dipole

compo- nents

along

the

long

molecular axis are very similar for the

compounds

of series I and II. As

SA phases

occur

in one series and

Sc phases

in the

other,

the model of Cabib and

Benguigui

cannot be

expected

to

apply

to

these systems. Furthermore the molecules of series I and II have a very similar molecular

shape.

An oxygen atom is somewhat smaller than a

CH2

group

[26],

which may make the molecules of series II about 0.5

A

shorter than the

corresponding

ones of series I.

Moreover the

Car

CC

angle

of 1080

(tetrahedral value)

is

replaced by

a

Car

OC

angle

of 120° which may lead to

a

slightly

more

pronounced zig-zag shape

for series I.

This difference between the series is reinforced

by

the

fact that the

mesophases

of series I occur at lower

temperatures,

thus

decreasing

the

flexibility

of the end

chains in series I as

compared

with series II. This

flexibility

can be

expected

to counteract the

zig-zag

form. Hence if these differences are

important

at

all,

it leads to a more

pronounced zig-zag

form for the molecules of series I than for series II. As the

SA phases

occur in series I and the

Sc phases

in series II it is

unlikely

that this difference is due to a

change

in the

repulsions

between the

zig-zag shaped

molecules.

On the other hand when

going

from series I to series II

two outboard

dipole

moments are introduced. Hence the results are at least

qualitatively

consistent with McMillan’s

dipole

model of the

Sc phase.

The fact

that an additional central

dipole

moment has no

influence on the

type

of smectic

phases (substitution azo-azoxy) requires

that the central aromatic cores of the molecules still rotate

relatively freely

in these sys- tems. It is

only

for the

dipoles

on the oxygen atoms that this rotation is not allowed. The

tendency

to form

an

Sc phase

is strong for series

II ;

there is no

SA phase

intermediate between the N and the

Sc phase.

As soon

as the

layered

structure is established the

phase

takes

the form of an

Sc phase

with a

relatively large

tilt

angle.

An

interesting

test on the

dipole

model of the

Sc phase

is

provided by

the results for series

III,

where

a weak

tendency

to form an

Sc phase

is found

(SA phase

intermediate between N and

Sc phase,

tilt

angle growing

with

decreasing temperature

from zero at the

SA Se transition).

In this series a

strong dipole

is

available

only

at one side of the

molecules,

while the

shape

of the molecules of series I or II is retained.

Assuming

that there is no

preference

for the asymme- tric molecules to be with the

polar

side up or

down,

McMillan’s model can still be

applied (see Fig. 6a).

However,

as the average distances between the

dipoles

has been

increased, TcA

is reduced

by

a factor 2

J2.

This decrease of

TcA

is less

pronounced

if the induced

dipole

moments due to the transverse

polarizabilities

are taken into account.

If,

for

simplicity,

the transverse

polarizability

of the molecule is assumed to be

represented by

two

point polarizabilities

a at

posi-

tions ±

d/2, equation (4)

must be

replaced by

where

n2

=

n2/2. Using

Boo = 2.5

(Ref. [27])

and

n2 N 4 x

1014 (Ref. [5])

we find

while a can be

expected

to be of the order of 1 x

10- 23 cm3 [27].

Hence the effect of the inclusion of a is an increase of

TCA by

about 50

%.

In the case of one end

dipole only,

we must also

consider the alternative situation of a

phase

that is a

FIG. 6. - The two possibilities for dipole interaction in the case of

one outboard dipole moment only; in situation (b) the smectic

layers are two-dimensional ferroelectrics.

(9)

1272

two-dimensional ferroelectric within the smectic

layers (see Fig. 6b).

In the context of the

present simple

models it is not useful to compare the relative

stability

of the

Sc phases depicted

in

figure

6a and

figure 6b,

which in

general

will

depend

on the ratio between the

asymmetric dipole potential

and the

symmetric

part of the total intermolecular

potential.

We

suggest

that

figure

6b

provides

a

possible

model for the

SF phase.

Like the

SF phase

the model has the

physical properties

of the

Sc phase.

In addition it will be ferroelectric or

anti-ferroelectric, depending

on the

sign

of the inter-

planar

interaction. The

compounds

studied here do not possess such an additional

phase.

These ideas would have to be tested on

compounds showing

an

Sc

and

an

SF phase [10],

which are

unfortunately

not

easily

available.

Finally

we come to the effect which the

symmetry

of the

shape

of the molecules has on the formation of smectic

phases.

When

comparing

series IV with series III we first consider some isometric

compounds

that have the same number of

CH2

groups but a

different

shape.

Compare

for

example :

We see that in

compounds

of the same

length

the

tendency

to form a smectic

phase

is greater in the case of a less

symmetric shape.

This conclusion was also arrived at

by

Malthete et

al.,

who studied several isometric series in detail

[28].

An

explanation

for this

effect has not yet been

given.

From tables III and IV we

see that there is no difference between the

type

of smec- tic

phases

that occur in series III and IV. In

particular

the

suggestion

that

Sc phases

are

preferentially

found

in

symmetrically

substituted

compounds [28, 29]

is not

confirmed, although

the results for series IV with

increasing n

indicate that if the deviation from symmetry

increases,

the

tendency

to form a smectic

phase

of some other type increases more

strongly

than the

tendency

to form an

Sc phase.

5. Conclusion. - We have shown that

alkyl and/or alkoxy

substituted azobenzenes may

show,

besides

the N

phase, SA

or

Sc phases

or

both, depending

on the

end substituents. The

results,

summarized in table

V,

suggest that the

repulsions

between the

zig-zag shaped

molecules do not

play a

dominant role in the formation of the

Sc phase.

The results are at least

qualitatively

in

agreement with McMillan’s

dipole

model of the

Sc phase, provided

the

asymmetric

molecules of series III and IV have no

preference

for

being

up or down. Otherwise the model

gives

a ferroelectric or

anti-ferroelectric

phase

that could

possibly

be iden-

tified with the

SF phase.

TABLE V

Summary oj’ the

results

Acknowledgments.

- The author wishes to thank Dr. J. Van der Veen for

making

the

compounds

of

series I and II available to

him,

and Mr. J. Boven for the

synthesis

of the

compounds

of series III and IV.

References [1] STEPHEN, M. J. and STRALEY, J. P., Rev. Mod. Phys. N 6 (1974)

617 ;

DE GENNES, P. G., The Physics of Liquid Crystals (Clarendon Press, Oxford) 1974.

[2] KOBAYASHI, K. K., Phys. Lett. 31A (1970) 125; J. Phys. Soc.

Japan 29 (1970) 101.

[3] MCMILLAN, W. L., Phys. Rev. A N (1971) 1238.

[4] LEE, F. T., TAN, H. T., YU MING SHIH and CHIA-WEI WOO, Phys. Rev. Lett. 31 (1973) 1117.

[5] MCMILLAN, W. L., Phys. Rev. A 8 (1973) 1921.

[6] WULF, A., Phys. Rev. A 11 (1975) 365.

[7] PRIEST, R. G., J. Physique 36 (1975) 437; J. Chem. Phys. 65 (1976) 408.

[8] CABIB, D. and BENGUIGUI, L., J. Physique 38 (1977) 419.

[9] VAN DER VEEN, J., DE JEU, W. H., GROBBEN, A. H. and BOVEN, J., Mol. Cryst. Liq. Cryst. 17 (1972) 291.

[10] DEMUS, D., DIELE, S., KLAPPERSTÜCK, M., LINK, V. and ZASCHKE, H., Mol. Cryst. Liq. Cryst. 15 (1971) 161.

[11] MAIER, W. and SAUPE, A., Z. Naturforsch. 14a (1959) 882;

15a (1960) 287.

[12] DE JEU, W. H. and VAN DER VEEN, J., Mol. Cryst. Liq. Cryst.

(in press).

[13] ZASCHKE, H. and SCHUBERT, H., J. Prakt. Chem. 315 (1973)

1113.

[14] DIANOUX, A. J., VOLINO, F., HEIDEMANN, A. and HERVET, H., J. Physique Lett. 36 (1975) L-275.

[15] MCMILLAN, W. L., Plenary Lecture at the Sixth Intern. Liq.

Cryst. Conf., August 23-27 (1976), Kent (Ohio).

[16] TAYLOR, T. R., ARORA, S. L. and FERGASON, J. L., Phys. Rev.

Lett. 25 (1970) 722.

[17] DE VRIES, A., J. Physique Colloq. 36 (1975) C1-1.

[18] WEYGAND, C. and GABLER, R., Ber. 71 (1938) 2399.

[19] See for example : SACKMANN, H. and DEMUS, D., Mol. Cryst.

Liq. Cryst. 21 (1973) 239.

[20] (a) DE JEU, W. H., unpublished results; (b) NEHRING J. and OSMAN, M. A., Z. Naturforsch. 31a (1976) 786.

(10)

[21] DEMUS, D. and SACKMANN, H., Z. Phys. Chem. (Leipzig) 222 (1963) 127.

[22] VAN DER VEEN, J., DE JEU, W. H., WANNINKHOF, M. W. M.

and TIENHOVEN, C. A. M., J. Phys. Chem. 77 (1973) 2153.

[23] ARNOLD, H., Z. Phys. Chem. (Leipzig) 226 (1964) 146.

[24] STEINSTRÄSSER, R. and POHL, L., Z. Naturforsch. 26b (1971)

577.

[25] MINKIN, V. I., OSIPOV, O. A. and ZHDANOV, Yu. A., Dipole

Moments in Organic Chemistry (Plenum Press, New York) 1970, p. 91.

[26] BONDI, A., Physical Properties of Molecular Crystals, Liquids

and Glasses (Wiley, New York) 1967.

[27] DE JEU, W. H. and LATHOUWERS, Th. W., Z. Naturforsch.

29a (1974) 905.

[28] MALTHÈTE, J., BILLARD, J., CANCEILL, J., GABARD, J. and JACQUES, J., J. Physique Colloq. 37 (1976) C3-1.

[29] GRAY, G. W. and GOODBY, J. W., Mol. Cryst. Liq. Cryst.

37 (1976) 157.

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